x uchun yechish
x = -\frac{21}{5} = -4\frac{1}{5} = -4,2
x=0
Grafik
Baham ko'rish
Klipbordga nusxa olish
5x^{2}+21x+4-4=0
Ikkala tarafdan 4 ni ayirish.
5x^{2}+21x=0
0 olish uchun 4 dan 4 ni ayirish.
x\left(5x+21\right)=0
x omili.
x=0 x=-\frac{21}{5}
Tenglamani yechish uchun x=0 va 5x+21=0 ni yeching.
5x^{2}+21x+4=4
ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.
5x^{2}+21x+4-4=4-4
Tenglamaning ikkala tarafidan 4 ni ayirish.
5x^{2}+21x+4-4=0
O‘zidan 4 ayirilsa 0 qoladi.
5x^{2}+21x=0
4 dan 4 ni ayirish.
x=\frac{-21±\sqrt{21^{2}}}{2\times 5}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 21 ni b va 0 ni c bilan almashtiring.
x=\frac{-21±21}{2\times 5}
21^{2} ning kvadrat ildizini chiqarish.
x=\frac{-21±21}{10}
2 ni 5 marotabaga ko'paytirish.
x=\frac{0}{10}
x=\frac{-21±21}{10} tenglamasini yeching, bunda ± musbat. -21 ni 21 ga qo'shish.
x=0
0 ni 10 ga bo'lish.
x=-\frac{42}{10}
x=\frac{-21±21}{10} tenglamasini yeching, bunda ± manfiy. -21 dan 21 ni ayirish.
x=-\frac{21}{5}
\frac{-42}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
x=0 x=-\frac{21}{5}
Tenglama yechildi.
5x^{2}+21x+4=4
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
5x^{2}+21x+4-4=4-4
Tenglamaning ikkala tarafidan 4 ni ayirish.
5x^{2}+21x=4-4
O‘zidan 4 ayirilsa 0 qoladi.
5x^{2}+21x=0
4 dan 4 ni ayirish.
\frac{5x^{2}+21x}{5}=\frac{0}{5}
Ikki tarafini 5 ga bo‘ling.
x^{2}+\frac{21}{5}x=\frac{0}{5}
5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.
x^{2}+\frac{21}{5}x=0
0 ni 5 ga bo'lish.
x^{2}+\frac{21}{5}x+\left(\frac{21}{10}\right)^{2}=\left(\frac{21}{10}\right)^{2}
\frac{21}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{21}{10} olish uchun. Keyin, \frac{21}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}+\frac{21}{5}x+\frac{441}{100}=\frac{441}{100}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{21}{10} kvadratini chiqarish.
\left(x+\frac{21}{10}\right)^{2}=\frac{441}{100}
x^{2}+\frac{21}{5}x+\frac{441}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(x+\frac{21}{10}\right)^{2}}=\sqrt{\frac{441}{100}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+\frac{21}{10}=\frac{21}{10} x+\frac{21}{10}=-\frac{21}{10}
Qisqartirish.
x=0 x=-\frac{21}{5}
Tenglamaning ikkala tarafidan \frac{21}{10} ni ayirish.
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